Chopping a Chebyshev Series

2015/12/06 by Jared L. Aurentz, Lloyd N. Trefethen, Aurentz, Jared L. +1 · 4 citations
Computer Science · #Digital Filter Design and Implementation #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1512.01803

openalex publication_date 2015/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function f(x) defined on an interval [a,b] is "rounded" to a prescribed precision by constructing a Chebyshev series and chopping it at an appropriate point. Designing a chopping algorithm with the right properties proves to be a surprisingly complex and interesting problem. We describe the chopping algorithm introduced in Chebfun Version 5.3 in 2015 after many years of discussion and the considerations that led to this design.

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